Teaching design of bicycle mathematics
Teaching objectives:
1. Understand the extensive relationship between mathematics and life by solving common problems about bicycles in life.
2. Through the process of "putting forward problems-analyzing problems-establishing mathematical models-practical application" to solve practical problems, the thinking method of using mathematics to solve practical problems is obtained.
3. By observing the structure of bicycle, analyzing its driving principle, a mathematical model is established.
4. Encourage students to innovate and cultivate their correct and reasonable design concepts.
Teaching emphases and difficulties:
Focus: the relationship between the speed of bicycle and its internal structure, and establish a mathematical model to solve the problem.
Difficulties: the influence of gear set on bicycle's progress, and the formation process of mathematical model.
teaching process
Expose the topic first 1. Teacher: How many students can ride bicycles in our class? Which students have their own bikes? What do you know about bicycles?
(Show real bicycles) Please introduce the structure of bicycles and the principle of bicycle travel.
2. Teacher: In this class, we will discuss the math problems in bicycles together. (blackboard writing topic)
Second, study the relationship between the speed and internal structure of ordinary bicycles.
1. Display: Xiaohong rides a bicycle with a tire diameter of 60dm from home to school. The wheel has just turned 100 turn. How many meters is it from Xiaohong's home to school?
Teacher: Tell me what you think. Summary: Driving distance = wheel circumference × number of laps
2. Teacher: If you want to know how far your bike can run once? What should we do?
Default 1: It can be measured directly.
Teacher: Before class, I asked my classmates to measure the distance traveled by the same bicycle once, and asked them to report the measurement results.
Summary: The measurement method is inaccurate and the error is large. Is there a more accurate method?
Default 2: Calculation method.
Teacher: How to calculate? Look at the pedal, the wheel turns several times, and then calculate the circumference of the wheel by the number of turns of the car. )
Teacher: So, if you ride a bike once, do you just go forward once? (No) (Seeing is believing, demonstrating)
When observing, think about it: who turned around while pedaling? Whose turn is the wheel actually turning?
Teacher: I want to know why the front gear rotates once and the rear gear rotates several times.
Teacher: According to this analysis, what is the key to solving the problem? (Turn the front gear once, and turn the rear gear several times. )
Teacher: Two gears connected to the same chain are like meshing gears. How does a tooth chain move when the front tooth rotates? How to move the rear gear? (The teacher slowly turns the front gear to observe)
Teacher: If the front gear turns two teeth, how can the rear gear move? What should I do if I turn five teeth in the front gear? 10 tooth? Did the students find any patterns? (Number of teeth of front gear × number of revolutions = number of teeth of rear gear × number of revolutions) What is the relationship between number of teeth of gears and number of revolutions? (inverse relationship)
3. Teacher: If the front gear of a bicycle has 48 teeth and the rear gear has 28 teeth, how many times does the front gear turn 1?
How to calculate it? Teacher: How to calculate the number of revolutions of the rear gear when the front gear rotates once?
Students write on the blackboard: number of revolutions of rear gear = number of teeth of front gear: number of teeth of rear gear.
Whose turn is the number of revolutions in the rear gear? So how do you calculate the number of revolutions required by the wheel? What's the distance for cycling once? Distance of pedaling for one cycle = wheel circumference × (number of teeth of front gear: number of teeth of rear gear)
If the tire diameter of these bicycles is 50 decimeters, please calculate the distance of one lap in groups.
4. Teacher: Which bicycle pedaled farthest? Observe the number of teeth of the front and rear gears carefully. Did you find anything?
Summary: The greater the difference between the front and rear gears, the farthest one lap can go.
Third, study the problem of variable-speed bicycles.
1, division; We studied math on an ordinary bike just now. What's the difference between a variable-speed bicycle and an ordinary bicycle? Do you know how it changes speed?
2. Show the main structural diagram of the variable-speed bicycle: there are two front gears and six rear gears.
How much speed can I change for group inquiry (1)?
(2) If you want to be the fastest, which combination would you choose?
2. Report. (12 speed, the greater the ratio, the farthest)
Fourth, thinking expansion.
Teacher: Actually, bicycles have not only math problems, but also mechanics problems that all junior high schools and senior high schools have to learn. Show various combination diagrams.
Discussion: A cyclist has to go through different sections in the race. How do you think the front and rear gears should be matched properly?
Verb (abbreviation for verb) consolidation exercise:
1. A bicycle has 26 front gears, 16 rear gears, and the wheel radius is 33cm. Can you figure out how far you can go by stepping on the pedal once? Xiaoming's home is about 500 meters away from school. How many laps does it take to run from home to school?
2. The front gear of bicycle has 28 teeth, and the rear gear has 14 teeth. Push 5 meters. Find the diameter of bicycle wheel. (Figures shall be kept to two decimal places)
Teaching design of bicycle mathematics
Teaching objectives:
1. Comprehensive knowledge to solve common mathematical problems in life.
2. Go through the basic process of "putting forward problems-analyzing problems-establishing mathematical models-solving-explaining and applying".
3. Feel the close connection between mathematics knowledge and daily life, experience the fun of learning and using mathematics, and stimulate the enthusiasm of learning knowledge.
Teaching emphasis: through practical activities, study the relationship between the speed of ordinary bicycles and their internal structure, and study how many speed combinations can be changed by variable-speed bicycles.
Difficulties in teaching: To study the relationship between the number of front and rear gears of ordinary bicycles and their revolutions.
Teaching preparation: multimedia courseware
Teaching process:
First, reveal the topic.
Today we are going to explore mathematics on the bike.
Second, study the relationship between the speed and internal structure of ordinary bicycles.
raise a question
How far does it take to ride a bike?
parsing problem
Method 1: Direct measurement (large error)
Method 2: Calculation method
solve problems
Principle of bicycle travel
What does the number of revolutions of the wheel matter?
Explore how many times the front gear turns and how many times the rear gear turns.
Cooperative investigation
How many teeth does the front gear rotate and how many teeth does the rear gear rotate? What if there are two teeth in the front gear? What about five teeth?
What pattern did you find?
Reporting and communication
What is the equal number of revolutions of the front and rear gears?
Conclusion: Number of teeth of front gear × number of revolutions of front gear = number of teeth of rear gear × number of revolutions of rear gear.
Number of revolutions of rear gear = number of teeth of front gear/number of teeth of rear gear.
mathematical modeling
Distance of bicycle pedaling once = number of teeth of front gear/number of teeth of rear gear × wheel circumference
application of knowledge
The diameter of bicycle wheel is 0.8m, the front wheel has 48 teeth, and the rear wheel has 16 teeth. How many meters can I run by bike? (
Third, study how much speed a variable-speed bicycle can change.
Observe the variable speed bicycle
Variable-speed bicycles generally have multiple front gears and multiple rear gears. For example, this variable-speed bicycle has two front gears and six rear gears.
Cooperative investigation
Show the forms in the book, communicate in groups and complete the forms.
Thinking: pedaling the same number of laps, the ratio of front and rear teeth is the combination of (), which makes the bicycle go farthest. This is
What?
Reporting and communication
Distance of bicycle pedaling once = tooth ratio × wheel circumference. When the wheel circumference is constant and the ratio of the number of teeth of the front gear to the number of teeth of the rear gear is the largest, the bicycle travels farthest.
Class summary Teacher: Students, what new gains have you made through today's practical activities?
Teaching Design and Reflection of Bicycle Mathematics
Teaching material analysis:
The comprehensive application of bicycle mathematics ranks behind the third unit "proportion" in the sixth grade mathematics volume of primary school. The purpose is to let students use the knowledge of circle, arrangement and combination, proportion and so on to solve practical problems. By solving the common problems about bicycles in life, we can understand the extensive relationship between mathematics and life, and go through the basic process of "putting forward problems-analyzing problems-establishing mathematical models-solving-explaining and applying", so as to obtain the thinking method of using mathematics to solve practical problems and deepen our understanding of what we have learned and their relationship.
Mathematics in bicycle mainly studies two problems: the relationship between the speed of ordinary bicycle and its internal structure; How much speed can a variable speed bicycle change?
Teaching philosophy:
Mathematics is an abstraction of the relationship between quantity and space in the objective world. It can be said that there is mathematics everywhere in life. "Mathematics Curriculum Standard" points out: "Mathematics teaching is a kind of mathematics activity, and teachers should closely contact with students' living environment and create vivid mathematics situations according to students' experience and existing knowledge ..." In the implementation of the new round of curriculum reform, the problem of "mathematics living" has been paid more and more attention and affirmed by educators. "Mathematics Curriculum Standard" clearly requires "let students feel the close connection between mathematics and life, and let students experience the mathematical process from the existing life experience." In life, from daily shopping to data processing in aerospace engineering, mathematics is everywhere. Students' learning mathematics is "a necessary tool in daily life to solve some simple practical problems by using the mathematical knowledge and methods they have learned." Guiding students to apply what they have learned can promote the formation of students' awareness of exploration and innovation and cultivate their preliminary practical ability.
The new curriculum standard mathematics textbook highlights the connection between mathematics and real life, and many teaching contents establish vivid life situations to help students learn and apply mathematics better. Mathematics in bicycle is to let students use what they have learned about circles, permutations and combinations, proportions and other knowledge to solve practical problems in bicycles. In the process of imparting mathematical knowledge and cultivating mathematical ability, teachers should naturally inject life content and guide students to learn to use what they have learned to serve their lives. This design is not only close to students' living standards, but also meets their psychological needs. At the same time, it also leaves some defects and expectations for students, so that they can connect their mathematics knowledge with real life more closely. Let mathematics teaching be full of life flavor and times color, really stimulate students' enthusiasm for learning mathematics, and cultivate students' independent innovation ability and problem-solving ability.
Teaching objectives:
1, let students use the knowledge of circle, permutation and combination, proportion and so on to solve practical problems.
2. Let students understand the extensive relationship between mathematics and life, get the thinking method of using mathematics to solve practical problems, and deepen their understanding of what they have learned and their relationship.
Teaching emphases and difficulties:
1, the mathematical model of the relationship between the speed of ordinary bicycle and its internal structure;
2. How much speed can a variable speed bicycle change?
teaching process
First, the new lesson introduction:
Teacher: Students, let's study math and use math. In our life, mathematics is everywhere. You see, there is a lot of math knowledge in our bike. Today, we are going to learn math by bike together.
Second, the new teaching:
1. Understand the structure of bicycles and travel to the far field.
There are three bicycles before class, an ordinary bicycle, a variable-speed bicycle and a children's bicycle. )
Teacher: Students, who knows how bicycles run? The teacher said, pushing the bike. Let the students observe, discuss and answer carefully. )
Health: It was the handlebar that pushed it.
Health: flow by wheels.
Health: the pedal drives the gear to rotate, and the gear drives the wheel to move forward.
Teacher: How do gears drive wheels? Please observe carefully. The teacher turned the pedal for the students to observe carefully. )
Answer through students' observation.
The teacher summed up the conclusion:
(1) step on your toes once and the front gear rotates once.
② The chain rotates with the front gear, the rear gear rotates with the chain, and the rear wheel rotates with the rear gear. The holes between the chains correspond to each tooth of the front and rear gears. When the front gear rotates one tooth, the rear gear must also rotate one tooth. The rear gear rotates as many teeth as the front gear rotates.
③ The rear gear rotates once and the wheel rotates once.
When teaching, we should closely contact with students' real life, guide students to carry out activities such as observation, operation and reasoning based on life experience and existing knowledge, and acquire basic mathematical knowledge and skills. ]
2. Study the relationship between the speed and internal structure of ordinary bicycles.
1) ask questions
Teacher: We have just learned the principle of bicycle travel. Who knows how far a bicycle can go once?
2 analyze the problem.
Ask students to discuss and solve problems in groups.